Mondriaan sparse matrix partitioning for attacking cryptosystems by a parallel block Lanczos algorithm - a case study

A case study is presented demonstrating the application of the Mondriaan package for sparse matrix partitioning to the field of cryptology. An important step in an integer factorisation attack on the RSA public-key cryptosystem is the solution of a large sparse linear system with 0/1 coefficients, which can be done by the block Lanczos algorithm proposed by Montgomery. We parallelise this algorithm using Mondriaan partitioning and discuss the high-level components needed. A speedup of 8 is obtained on 16 processors of a Silicon Graphics Origin 3800 for the factorisation of an integer with 82 decimal digits, and a speedup of 7 for 98 decimal digits.